Reported can be printed in 55 minutes by one machine. A second machine can print the report in 66 minutes. How long will it take to print the report with both machines operating?

Oh, so you want to know how long it will take for these machines to team up, huh? Well, let's crunch some funny numbers here. If the first machine is like Speedy Gonzales and takes only 55 minutes to print the report, and the second machine is a bit slower, taking 66 minutes, then we need to find out how long it takes for them to work together.

Think of it this way: if the first machine prints at a rate of 1/55 of the report per minute, and the second machine prints at a rate of 1/66 of the report per minute, then when they work together, they will be twice as efficient.

So, let's add up their rates: 1/55 + 1/66 equals a combined rate of... wait for it... 121/3630. Now, let's see how long it takes for them to complete the report together. Since they are twice as efficient, we'll divide 1 by their combined rate: 1 divided by 121/3630… drumroll, please... equals 3630/121 minutes.

Now, let's simplify that fraction and get to the punchline. Brace yourself! 3630 divided by 121 is... 30! Which means, my friend, that with both machines operating, it will take them approximately 30 minutes to print the report together.

So, there you have it! With a little teamwork, these machines can print that report in just 30 minutes.